Sliding Window Best Bid/Offer Spread

High-frequency algorithmic trading strategies at Citadel and Tower Research continually analyze streaming market quotes across rolling time windows. You are given two equal-length arrays of floating-point numbers, bids and asks, of size $N$, and an integer window size $K$ ($1 \le K \le N$).

For each sliding window of size $K$ ending at index $i$ ($K - 1 \le i < N$), the rolling best bid is $\max_{j \in [i - K + 1, i]} bids[j]$ and the rolling best ask is $\min_{j \in [i - K + 1, i]} asks[j]$. The effective spread of the window is defined as: $\text{spread}_i = \min_{j \in [i - K + 1, i]} asks[j] - \max_{j \in [i - K + 1, i]} bids[j]$

If $\text{spread}_i \le 0$, the market is in a crossed or locked condition, presenting an immediate latency arbitrage opportunity.

Your Task

Implement sliding_window_bbo_spread(bids: list[float], asks: list[float], k: int) -> tuple[list[float], list[int]] that returns:

1. A list of floating-point spreads for each window of length $K$ (rounded to 4 decimal places).
2. A list of window ending indices $i$ where a crossed/locked market was observed ($\text{spread}_i \le 0$).

Constraints

• $1 \le K \le N \le 10^5$
• $0.0 < bids[i] < 10^6$, $0.0 < asks[i] < 10^6$
• Execution must run in $\mathcal{O}(N)$ time.

Examples

bids = [100.0, 101.5, 102.0, 99.5]
asks = [103.0, 102.5, 101.8, 103.5]
k = 2
# Windows: i=1: min_ask=102.5, max_bid=101.5 -> spread=1.0
#          i=2: min_ask=101.8, max_bid=102.0 -> spread=-0.2 (crossed!)
#          i=3: min_ask=101.8, max_bid=102.0 -> spread=-0.2 (crossed!)
# Output: ([1.0, -0.2, -0.2], [2, 3])